Dear May,
We have tried Robert Karoly Clinic for the same reason, as of fully supporting natural birth and having water birth facility.
Unfortunately, the water birth facility is only a regular, small corner tub, that you could buy at any DIY store, so NOT suitable at all for water birthing. As it turned out, the really do not do water birthing, you can just relax there, before actual birth.
Nurses do not speak any english. Doctors do!
About supporting natural birth.... the doctor we have visited talked for 5 minutes about how they support it and the mother should be in focus and etc, but then she talked 20 MINUTES! about c-section and pain killers and hormones and how she also had a scheduled c-section etc... So we had huge doubts about their being natural.
The rooms were very basic, economy, hostel type, but clean!
We have visited the clinic 4 times for scheduled appointments and NEVER could go in on time. Minimum waiting was 1-hour but once we waited almost 2-hours before we have decided to leave the clinic.
We have not experienced any of their so marketed Moms first! and all natural attitude....
Take care!
Budapest Dad